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arXiv · 1211.5239

Estimation of extreme risk regions under multivariate regular variation

Juan-Juan Cai·John H. J. Einmahl·Laurens de Haan
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Abstract

When considering d possibly dependent random variables, one is often interested in extreme risk regions, with very small probability p. We consider risk regions of the form ${\mathbf{z}\in\mathbb{R}^d:f(\mathbf{z})\leq\beta}$, where f is the joint density and $\beta$ a small number. Estimation of such an extreme risk region is difficult since it contains hardly any or no data. Using extreme value theory, we construct a natural estimator of an extreme risk region and prove a refined form of consistency, given a random sample of multivariate regularly varying random vectors. In a detailed simulation and comparison study, the good performance of the procedure is demonstrated. We also apply our estimator to financial data.

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Juan-Juan Cai, John H. J. Einmahl, Laurens de Haan. 2012-11-22. Estimation of extreme risk regions under multivariate regular variation. https://doi.org/10.1214/11-aos891

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